Representing Boolean Functions Sumofproducts Expansions 1 M AL

Representing Boolean Functions Sum-of-products Expansions 1 M. AL- Towaileb

Literal & Minterm DEFINITION 1 2 M. AL- Towaileb

EXAMPLE 2 Find a minterm that equals 1 if x 1=x 3=0 and x 2=x 4=x 5=1, and equals 0 otherwise Solution: The minterm has the correct set of values. 3 M. AL- Towaileb

Sum-of-products Expansions The sum of minterms that represents the function is called the sum-of-products expansion or the disjunctive normal form of the Boolean function. 4 M. AL- Towaileb

EXAMPLE 3 Solution: 5 M. AL- Towaileb

Second, we can construct the sum-of-products expansion by determining the values of F for all possible values of the variables x, y, and z. These values are found in Table 2. The sum-of products expansion of F is the Boolean sum of three minterms corresponding to the three rows of this table that give the value 1 for the function. This gives 6 M. AL- Towaileb

Functional Completeness • Every Boolean function can be expressed as a Boolean sum of minterms. • Each minterm is the Boolean product of Boolean variables or their complements. • This shows that every Boolean function can be represented using the Boolean operators. , +, and -. • Because every Boolean function can be represented using these operators we say that the set {. , +, - } is functionally complete. • We can eliminate all Boolean sums using the identity • Similarly, we could eliminate all Boolean products using the identity 7 M. AL- Towaileb

Homework Page 760 • 1(b, c) • 2(a, d) • 3(a, d) • 7(c) • 12(a, c) 8 M. AL- Towaileb